I gained some great intuition from http://matrixmultiplication.xyz/ http://matrixmultiplication.xyz/ and (of all things) a paper named "An Introduction to Quant

I gained some great intuition from http://matrixmultiplication.xyz/ http://matrixmultiplication.xyz/ and (of all things) a paper named "An Introduction to Quantum Computing"[0]. Page 3 of that paper lays out matrix multiplication (e.g.: applying a "transformation matrix" in the spatial parlance of 3blue1brown's videos) as a traversal of a directed graph. This isn't super readable (it's from my notes to self), but my intuition is: Matrix multiplication is a graph traversal: * Each i,j in transform matrix (on left) pulls N (the value at that index) times the j-th value in the input vec (on right) into the i-th output vec index * This is equivalent to an N weighted vertex from the j-th node to i-th node, so i takes N of j's previous value * The input (right side) is a matrix? It's just multiple column vectors next to each other, repeat the above process and make a new output vector for each iteration [0]: https://arxiv.org/abs/0708.0261 https://arxiv.org/abs/0708.0261